Question

a ball is thrown into the air with an upward velocity of 80 feet per second. the function h = - 16t² + 80t models the height h, in feet, of the ball at time t in seconds. when will the ball reach the ground? after 3 seconds after 6 seconds after 5 seconds after 4 seconds

Explanation:

Step1: Set height h to 0

When the ball reaches the ground, its height $h = 0$. So we set the function $h=-16t^{2}+80t = 0$.

Step2: Factor out the common - factor

Factor out $-16t$ from the left - hand side of the equation: $-16t(t - 5)=0$.

Step3: Use the zero - product property

The zero - product property states that if $ab = 0$, then either $a = 0$ or $b = 0$. So we have two cases:
Case 1: $-16t=0$, which gives $t = 0$. This represents the time when the ball is initially thrown.
Case 2: $t - 5=0$, which gives $t = 5$. This is the time when the ball returns to the ground.

Answer:

after 5 seconds